Three essays on the evaluation of informality in the Chilean labor market using high-dimensional methods

Motivation

Analyzing informality in the Chilean labor market is complex.

We explore informality from a multidimensional perspective in three stages using hig-dimensional statistical tools:

1. Decision to work informally.
2. Monetary gain or loss from working formally or informally.
3. Monetary gain or loss from working formally or informally by status in employment.

Introduction

Informal employment rate in Chile: 27.5%.

Microeconomics factors:

• Race, education, financial acces, working in skilled occupations (Gunter 2017).
• Rural area, gender, marital status, age, years of schooling, occupation, economic activity (Angel-Urdinola et al. 2012).
• Individual characteristics, labor market discrimination, economic crises (Nordman, Rakotomanana, and Roubaud 2016).
• Age, marital status, number of family members working in the informal sector, years of schooling, occupation, industry, and region (Amuedo-Dorantes 2004).

Definition of Informal Worker: ILO Definition

• Unpaid family workers: all.
• Employees: not paid social security contributions or health insurance.
• Employers: firm has five or fewer employees nationwide.
• Own-account workers: their occupation is not classified as “Members of the executive and legislative bodies and managerial personnel of the public administration and companies’’,”Scientific and intellectual professional” or “Technicians and mid-level professionals”.

Methodology: Probit model

where,

• \(y_{i}\) represents informal employment participation, equal to one if individual \(i\) is an informal worker and zero otherwise.
• \(\boldsymbol{x}_{i}\) is an individual characteristic vector selected by adaptive lasso.

Results: Number of controls selected by ADAPTIVE LASSO

Conclusions

Decision to work informally depends not only on individual-level characteristics in a linear form, but also on their interactions.

Cross-category interactions consistently decrease the probability of working informally:

• Contract Type \(\times\) Administrative Zone (All, men, and women).
• Contract Type \(\times\) Firm Size (All, men, and women).
• Contract Type \(\times\) Nationality (Men).
• Firm Size \(\times\) Administrative Zone (Women).
• Contract Type \(\times\) Sexual Orientation (Women).

Marital Status \(\times\) Contract Type increases the probability of working informally for women.

Policy interventions should take account heterogeneity of subgroups for the distributive efficiency of public resources.

Motivation and Literature Review

Raw wage gap between formal and informal workers: 60.3%

Wage premium formal workers

• Education, experience, work in large enterprises (Balcar 2012; Bargain and Kwenda 2011, 2014; Cho and Cho 2011; Kumar and Pandey 2021; Meghir, Narita, and Robin 2015)

Wage penalty informal workers

• Lower education, women, younger workers, live in rural area (Angel-Urdinola et al. 2012; Falco et al. 2011; Maurizio 2012; Rosser, Rosser, and Ahmed 2000; Tansel, Keskin, and Ozdemir 2020)

Motivation and Literature Review

Informal worker definition following ILO definition

• Unpaid family workers: all.
• Employees: not paid social security contributions or health insurance.
• Employers: firm has five or fewer employees nationwide.
• Own-account workers: their occupation is not classified as “Members of the executive and legislative bodies and managerial personnel of the public administration and companies’’,”Scientific and intellectual professional” or “Technicians and mid-level professionals”.

Methodology: ADAPTIVE LASSO

Following Adaptive Least Absolute Shrinkage and Selection Operator (adaptive lasso) methodology proposed by Zou (2006).

\[ \begin{equation*} \DeclareMathOperator*{\argmin}{arg\,min} \boldsymbol{\hat{\beta}}^{*(n)}_{\mathsf{ALASSO}} = \argmin_{\{\beta_{1},\dots, \beta_{K} \} }\Bigg\| \boldsymbol{y}-\sum_{j=1}^{K}\boldsymbol{x}_{j}\beta_{j}\Bigg\|^{2}+\lambda\sum_{j=1}^{K}\hat{w}_{j}|\beta_{j}|, \end{equation*} \] where \(\lambda\) is a non–negative regularization parameter selected using cross–validation, \(\boldsymbol{\widehat{w}}=\{ \widehat{w}_{1},\dots,\hat{w}_{K} \}\) is a vector of weights defined as \(\boldsymbol{\hat{w}}= \frac{1}{|\boldsymbol{\hat{\beta}_{RIDGE}}|^{\gamma}}\), with \(\gamma = 1\).

Our relevant subset of predictors \(A^{*}_{n}\) corresponds to the non–zero parameters for formal and/or informal workers: \(A^{*}_{n}=\{j:\hat{\beta}^{F}_{\mathsf{Alasso}, j}\neq 0 \; \vee \; \hat{\beta}^{I}_{\mathsf{ALASSO}, j}\neq 0 \}\).

The Sparse Matrix

The Sparse Matrix: Interpreting the Results

Results: Controls selected

Conlcusions

Nonlinearity relevant in the wage structure of formal workers amd informal workers.

Wage gap between formal and informal workers is mainly explained by nonlinearities.

Data

Data used: eps 2004, eps 2006, eps 2009, and eps 2015.

17.78% of people were in informal employment in Chile between 2004 and 2015.

Informal workers:

• Unpaid family workers (2.05%).
• Salaried workers (8.49%).
• Employers (27.39%).
• Self-employed workers (62.07%).

We use 38 variables (individual and job characteristics) to create a second-degree polynomial.

Methodology: OLS POST-LASSO (Belloni et al. 2016)

\[ \begin{equation*} y_{it}=\boldsymbol{x}_{it}^{T}\boldsymbol{\beta}+\hat{\lambda}_{it}+d2_{t}\hat{\lambda}_{it}+\cdots+dT_{t}\hat{\lambda}_{it} + \mu_{i}+\varepsilon_{it} \end{equation*} \] where,

• \(\hat{\lambda}_{it}\) corresponds to the Inverse Mills Ratio for the individual \(i\) in time \(t\).
• \(\boldsymbol{x}_{it}\) is a characteristics vector for the individual \(i\) in time \(t\) from the Sparse Matrix.
• \(d2_{t}\) to \(dT_{t}\) are time dummy variables.

Number of controls selected and estimated by OLS Post-LASSO

Conclusions

Nonlinear effects are relevant in the log wage generation process for employers, self-employed, and salaried workers.

Public policies should take account the heterogeneity of labor market and consider individual and job characteristics that affect income generation.